Abstract
Energy momentum tensor (EMT) characterizes the response of the vacuum as well as the thermal medium under the color electromagnetic fields. We define the EMT by means of the gradient flow formalism and study its spatial distribution around a static quark in the deconfined phase of SU(3) Yang-Mills theory on the lattice. Although no significant difference can be seen between the EMT distributions in the radial and transverse directions except for the sign, the temporal component is substantially different from the spatial ones near the critical temperature $T_c$. This is in contrast to the prediction of the leading-order thermal perturbation theory. The lattice data of the EMT distribution also indicate the thermal screening at long distance and the perturbative behavior at short distance.
Highlights
To study complex quantum systems such as the YangMills (YM) theory, it is customary to introduce test probe(s) and analyze the response
No significant difference can be seen between the energy-momentum tensor (EMT) distributions in the radial and transverse directions except for the sign, the temporal component is substantially different from the spatial ones near the critical temperature Tc
The purpose of the present paper is to extend the above idea and to explore the EMT distribution around a static quark in YM theory
Summary
To study complex quantum systems such as the YangMills (YM) theory, it is customary to introduce test probe(s) and analyze the response. The Wilson loop is one of such probes whose measurement in YM theory provides information on the static quark-antiquark system that is closely related to the confinement property in YM vacuum [1]. Thanks to the recent development of the gradient-flow method [2,3,4] and its application to the energy-momentum tensor (EMT) T μνðxÞ [5,6,7,8], it became possible to study the gauge-invariant structure of the flux tube between the quark and antiquark in the confining phase through the spatial distribution of EMT under the Wilson loop [9,10].
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